The present invention relates to magnetic resonance imaging and in particular to the use of adiabatic pulses for changing magnetic moments.
FIG. 1 is a schematic diagram of an MRI (Magnetic Resonance Imaging) system as well known in the art. A patient 20 is placed into a powerful, axial, homogenous magnetic field generated by a magnet 22. The tissues which make up patient 20 contain many hydrogen nuclei, some of which have magnetic moments aligned with the magnetic field. When an aligned hydrogen atom is irradiated with RF radiation of a suitable frequency, transmitted by an RF transmitter 24, its magnetic moment changes direction relative to the field. The new direction of the magnetic moment is not stable, so after a time the magnetic moment reorients itself back to the magnetic field direction. During this reorientation, the hydrogen atom emits RF radiation, which radiation is detected by RF receiver 30.
The RF radiation is generated by hydrogen nuclei which have a magnetic moment at an angle to the magnetic field, which moment precesses about the axial field direction. The RF irradiation tends to align the magnetic moments so they are all in phase with each other such that their individual contributions to the RF signal are additive.
As can be appreciated, tissues which have a high concentration of hydrogen nuclei will emit a higher amplitude of RF energy than tissues which have a low concentration of hydrogen nuclei. In addition, different body tissues can be characterized by their T1 and T2 relaxation times, which can be imaged using various MRI imaging sequences. Also, the emission frequency depends on the chemical bonds of the hydrogen atom, so the emission frequency can be analyzed to detect different chemicals in the body, in what is known as MRI spectroscopy.
In order to generate an image of a body portion, the spatial origin of the acquired RF signals must be determined. In a typical coordinate system the Z coordinate is in the direction of the longitudinal axis of patient 20 (and the direction of the DC magnetic field) and the X and Y axes are perpendicular to it. Some methods of MRI imaging limit the image acquisition to one slice in the X-Y plane at a time, by what is called slice selection. The RF frequency, which causes the magnetic moments of hydrogen nuclei to change their orientations, is functionally dependent on the intensity of the magnetic field. A Z gradient coil 26 imposes a gradient, in the Z direction, on the Z directed field generated by magnet 22, so that each axial slice of patient 20 is subjected to a different Z-directed magnetic field. RF transmitter 24 transmits a narrow band RF signal, which affects the orientation of hydrogen nuclei in only a narrow body portion (slice) 27 and hence causes emission of RF radiation from portion 27 alone.
In order to differentiate between RF signals emitted by different segments of portion 27, a Y gradient coil 32 is typically used to momentarily create a Y gradient in the Z directed magnetic field of magnet 22. This Y gradient is created before readout, described below. Nuclei in segments of portion 27 which have a momentary increase in the locally applied magnetic field advance in phase, since the precession speed is dependent on the field strength, while nuclei which have a momentary decrease in the locally applied magnetic field retreat in their phase. Thus, portion 27 is divided into first parallel strips (in the Y direction), each of which emits RF radiation at a different phase.
The X coordinate of an RF emission is determined during a stage called readout. To perform readout, the Z directed magnetic field including portion 27 is varied in the X direction, using an X gradient coil 28, so that portion 27 is substantially divided into second parallel strips (in the X direction) each of which has a different local magnetic field strength. Since the frequency of the emitted RF radiation is directly dependent on the local field intensity, each of the second parallel strips emits radiation at a different frequency. An image can be reconstructed by acquiring a plurality of RF signals during readout, each of which has a different Y gradient phase encoding and a X gradient frequency encoding, and performing a two-dimensional FFT (fast Fourier transform) on the acquired signals. It should be appreciated that many different types of MRI imaging sequences are known in the art, including sequences where the imaged nucleus is not Hydrogen.
FIG. 2A is a schematic diagram showing the interaction between a magnetic moment 40 of a sample and a static Z magnetic field 42 having a magnitude B0. Field 42 causes magnetic moment 40 to become aligned with the +Z direction and to spin at an angular velocity xcfx890=xcex3B0 around the Z direction, where y is the gyromagnetic ratio of the inspected nucleus. xcfx890 is also called the Larmor frequency. FIG. 2B illustrates an example where moment 40 is also subjected to an RF magnetic field 44 having a magnitude B1 and a frequency xcfx89. The most convenient frame of reference in which to describe the effect of RF field 44 is a rotating frame of reference, having an origin coinciding with moment 40 and rotating in the X-Y plane at an angular velocity xcfx89. The following description is based on such a rotating frame. The total interaction between RF field 44, static field 42 and moment 40 may be described by an effective magnetic field vector Beff which interacts with moment 40. Beff created by RF field 44 comprises an X-component xcex3B1 (which defines the component of Beff in the X-Y plane) and a Z component xcex94xcfx89=xcfx89xe2x88x92xcfx890. The interaction between Beff and moment 40 is such that moment 40 precesses around Beff at an angular frequency |xcex3Beff|. RF field 44 has X, Y and Z components. However, the RF field component in the Z direction generally has a smaller magnitude than B0, so it may be ignored.
The effect of a (varying) RF magnetic field on a magnetic moment is generally described by a well known differential equation, the Bloch equation, which is described in detail in C. P. Slichter, xe2x80x9cPrinciples of Magnetic Resonance,xe2x80x9d 3rd ed. Springer-Verlag, Berlin, 1992, the disclosure of which is incorporated herein by reference. The following description is correct for short time scales (pulse duration is shorter than a typical T2 of the human tissues), where the relaxation terms in the Bloch equation may be ignored.
When combining the effects of RF field 44 and static field 42, notice must be taken of the relationship between xcfx89 and xcfx890. FIG. 3 shows the case where xcfx89=xcfx890. In this case, the Beff interacting with moment 40 is wholly in the X direction (with an amplitude determined by the amplitude of RF field 44). The effect of such a vector on moment 40 is that moment 40 precesses around the X axis (i.e., in the Z-Y plane in the case that moment 40 was originally aligned with the +Z direction).
In MRI terminology, a pulse using an RF field with xcfx89=xcfx890 is called an AM pulse. This type of pulse has a frequency, equal to the Larmor frequency (xcfx890). Its amplitude changes with time. An AM pulse may be used to effect inversion of a moment 40, which moment is originally aligned with the Z direction, in the following manner: an RF field 44 having a known strength is applied to moment 40; and once moment 40 has made a 180xc2x0 rotation (in the Y-Z plane), i.e., moment 40 is inverted, RF field 44 is turned-off.
The precession velocity of moment 40 about rotating axis X is linearly dependent on the amplitude of RF field 44. An important result of this linear dependency is the sensitivity of the AM pulse to RF field inhomegenities, which may be characteristic of an RF coil which generates RF field 44 or by local inhomegenities caused by the sample being imaged. As an example of this sensitivity to field inhomegenities, if two similar samples are subjected to the same RF pulse duration but the RF field is 120% as intense at one sample than at the other sample, the magnetic moment of one sample will complete 216xc2x0 of rotation, while the magnetic moment of the other sample will complete 180xc2x0 of rotation.
The effect of an RF field which is not at the Larmor frequency can be appreciated by comparison with the effect of an AM pulse. In general, an AM inversion pulse operates by rotating moment 40 by 180xc2x0 in a plane perpendicular to Beff. Normally, this plane is the Y-Z plane, since Beff is aligned with the X direction. Referring back to FIG. 2B, if xcex94xcfx89 is small, moment 40, rotated 180xc2x0 around Beff is still substantially aligned with the Z axis. However, if xcex94xcfx89 is large, moment 40 will not be aligned with the Z axis after the inversion (it will point somewhere else in space), and as such cannot be considered inverted. This effect of off-resonance frequencies on the inversion characteristics of moment 40 can be used for slice selection, where a Z gradient field is applied to a sample during RF irradiation, so that only one slice of the sample is irradiated at its Larmor frequency. Thus, only a portion of the sample (the slice) is properly inverted by the RF irradiation, while other portions are only partially inverted (or not inverted at all).
An FM pulse utilizes an RF field having a varying frequency to invert the magnetic moments in a sample even in the presence of RF field inhomogeneities. FIG. 4 illustrates the effect of an FM pulse on inversion of a magnetic moment. Beff at the start of the pulse is aligned with the Z direction and very slowly moves to the xe2x88x92Z direction along a trajectory 46 (i.e., xcex8 changes slowly). The term trajectory is used to describe the path traced by the tip of vector Beff throughout the pulse. Mathematically, this describes the functional dependence between xcex94xcfx89 and xcex3B1. If the movement of Beff is slow enough, moment 40 will follow the movement of Beff until Beff is aligned with the xe2x88x92Z direction. The term xe2x80x9cvery slowxe2x80x9d means that the precession velocity (|xcex3Beff|) is much larger than the angular velocity of Beff,{dot over (xcex8)}. Mathematically this is formulated by the adiabatic condition as |xcex3Beff| greater than  greater than |{dot over (xcex8)}|.
FM pulses of this type are commonly called adiabatic pulses, since the (slow) movement of the precession axis Beff has little effect on the (fast) precession of moment 40 about it. One important result of this adiabatic condition is that the inversion is substantially insensitive to the strength of RF field 44, within certain limits. Increasing the strength of RF field 44 by 10% will cause Beff to follow a trajectory 47 instead of trajectory 46. This change in trajectory will have negligible effect on the inversion, since the strength of RF field 44 affects mainly the precession velocity of the moment and has a small effect on the angular velocity {dot over (xcex8)} of Beff. So long as the adiabatic condition is fulfilled, the FM pulse will operate (invert moment 40) in substantially the same manner. As can be appreciated, a magnetic moment will be inverted by an adiabatic FM pulse if
(a) the magnetic moment is xe2x80x9ccapturedxe2x80x9d by Beff so that it tracks Beff, and
(b) the magnetic moment does not xe2x80x9cescapexe2x80x9d Beff prematurely. This requires that the adiabatic condition be fulfilled over the entire duration of the FM pulse.
Solutions of the Bloch equation can be used to describe RF pulses which invert magnetic moments. One very important characteristic of inversion pulses is their frequency selectivity. If an inversion pulse is very frequency sensitive (selective), it can be used to define a slice with sharp boundaries (slice selection, described above). The degree of frequency selectivity is an important parameter of the resolution possible in an MRI system (which resolution is NOT dependent on the wavelength of the radiation). In addition, a highly selective pulse can be used to selectively invert Hydrogen nuclei associated with different materials in a single slice, where each material has a different xcfx890.
One case where frequency selection is important is in imaging the breast, where it is desirable to suppress the contribution of adipose tissue so that the signal to noise ratio of water based tissues is improved. In some cases, suppression of silicone implants is also desirable. FIG. 7 is a graph showing the relationship between the Larmor frequencies of fat and of water. It should be appreciated that the difference between the peaks is only 3.5 ppm (parts per million). FIG. 8 shows a pulse/gradient sequence in which fat is suppressed. An inversion pulse 50, which is very frequency selective, so that it only inverts fat in the slice, is applied to the tissue. After a waiting period 52 (dependent on the T1 relaxation time of the fat), in which a sharp gradient called a spoiler gradient may be applied, the magnetic moment of the fatty tissue is substantially zero (neither +Z nor xe2x88x92Z). At this point in time an imaging sequence 54 is applied for imaging the tissue, in which sequence the radiation emitted by adipose tissue is substantially reduced.
It can be appreciated that fat inversion pulses should be highly frequency selective, so that they can distinguish between the proximal water and fat Larmor frequencies. xe2x80x9cHybrid Methods of Chemical-Shift Imagingxe2x80x9d, by Jerzy Szumowski, Jane K. Eisen, Simon Vinitski, Peter W. Haake and Donald B. Plewes, in xe2x80x9cMagnetic Resonance in Medicinexe2x80x9d vol. 9, pp. 379-388, published by Academic Press, Inc., 1989, the disclosure of which is incorporated by reference, describes several frequency selective imaging methods for suppressing fat. In one method, shown in FIG. 2 of the above paper, the amplitude of the water signal is detrimentally affected by the fat suppression.
Frequency selection in AM pulses, by the effects of off-resonance irradiation, has been described above with respect to FIG. 2B. Off-resonance behavior of FM inversion pulses can be divided into three types: inversion (FIG. 5), transition (FIG. 6A) and non-inversion (FIG. 6B). FIG. 5 shows the effect of an FM pulse on a sample, where the sample is slightly off-resonance (the Larmor frequency is slightly different from the RF frequency about which the inversion pulse is designed). The result is that trajectory 46 is shifted along the Z axis to a new trajectory 60. It can be appreciated that trajectory 60 still maintains the adiabatic condition, namely, that {dot over (xcex8)} is much smaller than the precession velocity. Thus, the inversion pulse still functions in many cases of small off-resonances, such as in small variations in the static magnetic field.
FIG. 6A shows the transition behavior of the pulse. Trajectory 46 is shifted to a new trajectory 62. Attention is directed to a region 64 of trajectory 62. In region 64, the magnitude of Beff is considerably increased while {dot over (xcex8)} varies slightly relative to a corresponding region of trajectory 46, so the adiabatic condition is still fulfilled. As a result, xe2x80x9ccapturexe2x80x9d by and tracking of Beff by moment 40 is facilitated. However, in a region 66 of trajectory 62, the magnitude of Beff is significantly smaller than in the corresponding portion of trajectory 46, thereby violating the adiabatic condition. As a result, a magnetic moment which is too far from resonance will stop tracking and xe2x80x9cescapexe2x80x9d from Beff. In the other off-resonance condition, where trajectory 46 is shifted in the xe2x88x92Z direction, off-resonance nuclei will stop tracking at the beginning of the trajectory, as soon as the adiabatic condition is violated. Thus, when the sample is too far off-resonance, the pulse will not properly invert the sample.
FIG. 6B shows the non-inversion behavior of the pulse at large off-resonances. When trajectory 46 is shifted far enough away from its original position (as shown in FIG. 4) to a new trajectory 67, the FM pulse is once again adiabatic. However, the operation of the pulse in this case is non-inverting, since the moment is shifted away from the +Z axis and then back again to the +Z axis.
The range of frequencies over which the pulse changes from an inverting pulse to a non-inverting pulse is called the transition. Narrow transitions imply sharp slice selections.
One FM pulse which has excellent RF field inhomogeneity stability and has a narrow transition is a sech/tanh pulse. The sech/tanh pulse is further described in M. S. Silver, R. I. Joseph and D. I. Hoult, xe2x80x9cSelective Spin Inversion in Nuclear Magnetic Resonance and Coherent Optics through an Exact Solution of the Bloch-Riccati Equation,xe2x80x9d Physical Review A, Vol. 31, pp. 2753-2755, 1985, the disclosure of which is incorporated herein by reference. xe2x80x9cSech/tanhxe2x80x9d is a notation which describes the modulation functions of xcex3B1 and xcex94xcfx89 (respectively) as a function of time (which determine Beff with respect to a certain Larmor frequency). The trajectory of a sech/tanh pulse is a half-ellipse, as is the trajectory of a sin/cos pulse. In an AM pulse, where only the amplitude is varied, only one component (the xcex3B1 component) is described, e.g., a xe2x80x9csincxe2x80x9d pulse. FIG. 9 shows the frequency selection profile of a sech/tanh pulse having a transition region 68, an inverted region 70 and a non-inverted region 71. Two important parameters of the inversion pulse are the transition and inversion bandwidths.
The adiabatic condition can also be affected by the duration of the FM pulse. In a fast pulse the angular velocity of Beff is higher than in an otherwise similar slow pulse, since the same trajectory is traversed in less time. If the angular velocity is higher, the transition width is increased compared to a slower pulse, since the faster pulse is less adiabatic.
xe2x80x9cAnalytic Solution to the Two-State Problem for a class of Coupling Potentials,xe2x80x9d by A. Bambini and P. R. Berman, in xe2x80x9cPhysical Reviewxe2x80x9d, Vol. 23, No. 5, pp. 2496-2501, published by the American Physical Society, May 1981, the disclosure of which is incorporated herein by reference, describes an AM pulse with an asymmetric temporal envelope which results in an asymmetric frequency response.
One object of some embodiments of the present invention is to provide a method of achieving narrower transitions in MRI adiabatic inversion pulses. In one embodiment of the invention this is achieved by providing an inversion pulse having an asymmetric magnetization profile. Thus, one transition is narrower than the other transition. Preferably, the pulse can be controlled to effect a trade off between the widths of the two transitions.
Another object of some embodiments of the present invention is to provide a method of selective fat inversions, whereby a pulse having asymmetric magnetization is configured so that its narrow transition area falls in between the Larmor frequencies of water and fat. Thus, one is inverted and the other is not.
In some embodiments of the invention, an asymmetric magnetization profile is achieved using an asymmetric pulse. This type of pulse is preferably asymmetric in that the angular velocity of the effective magnetization filed vector is not mirrored through 90xc2x0 for any of the in-slice regions, for at least some of the angles. Preferably, at least 10% of the angles have asymmetric angular velocities. Alternatively, at least 20% of the angles are not mirrored. Alternatively, at least 40% of the angles are not mirrored. Alternatively, at least 70%, or even 80% of the angles are not mirrored.
In accordance with a preferred embodiment of the present invention, a more general solution of the Bloch equation is provided which may be used to design NMR/MRI pulses and which incorporates previous known solutions such as certain AM pulses and the sech/tanh pulse. This solution was obtained by solving a hyper-geometric equation derived from the Bloch equation, hence, the new pulse is designated a hyper-pulse.
The solution is best described with respect to a reference frame which is rotating at the instantaneous frequency of the RF pulse. A pulse, designed in accordance with such a solution, has an effective magnetic-field vector xcfx89e=xcex3Beff=(xcfx891(t),0,xcfx89(t)xe2x88x92xcfx890). The components are given by the following parametric equations in z:                                                                         ω                x                            =                                                ω                  1                                =                                                      Ω                    0                                    ⁢                                      xe2x80x83                                    ⁢                                                                                    z                        ⁡                                                  (                                                      1                            -                            z                                                    )                                                                                                            az                      +                      b                                                                                                                                                              ω                y                            =              0                                                                                          ω                z                            =                                                ω                  -                                      ω                    0                                                  =                                                                                                    cz                        +                        d                                                                    az                        +                        b                                                              ⁢                                          xe2x80x83                                        -                                          ω                      0                                                        =                                      Δ                    ⁢                                          xe2x80x83                                        ⁢                    ω                                                                                                          (        1        )            
where a, b, c, d and xcexa90 are parameters (real numbers). The time variable t is mapped by the variable z. When z advances from 0 to 1, t advances from xe2x88x92∞ to +∞. Variables t and z are related by the following equation:                     t        =                  ln          ⁢                      xe2x80x83                    ⁢                                    z              b                                                      (                                  1                  -                  z                                )                                            a                +                b                                                                        (        2        )            
The final distribution of the magnetization in the sample, assuming the initial magnetization of the sample was at equilibrium in the Z direction; is:                               M          z                =                                                            sinh                ⁢                                  xe2x80x83                                ⁢                π                ⁢                                  xe2x80x83                                ⁢                r                ⁢                                  xe2x80x83                                ⁢                sinh                ⁢                                  xe2x80x83                                ⁢                π                ⁢                                  xe2x80x83                                ⁢                v                            +                              cos                ⁢                                  xe2x80x83                                ⁢                2                ⁢                π                ⁢                                  xe2x80x83                                ⁢                q                                                    cosh              ⁢                              xe2x80x83                            ⁢              π              ⁢                              xe2x80x83                            ⁢              r              ⁢                              xe2x80x83                            ⁢              cosh              ⁢                              xe2x80x83                            ⁢              π              ⁢                              xe2x80x83                            ⁢              v                                ⁢                      xe2x80x83                    ⁢          where                                    (        3        )                                                                    r              =                              d                -                                                      ω                    0                                    ⁢                  b                                                                                                        v              =                                                (                                      c                    +                    d                                    )                                -                                                      ω                    0                                    ⁡                                      (                                          a                      +                      b                                        )                                                                                                                          q              =                                                1                  2                                ⁢                                  xe2x80x83                                ⁢                                                                            Ω                      0                      2                                        -                                                                  (                                                  c                          -                                                                                    ω                              0                                                        ⁢                            a                                                                          )                                            2                                                                                                                              (        4        )            
It should be noted that q may be an imaginary number, in which case, the cosine in equation (3) becomes a hyperbolic cosine. Mz is normalized to M0, the initial magnetization in the +Z direction.
If a=0, the solution results in a sech/tanh pulse. If c=d=0, the solution is an AM pulse. However, as can be seen, these two solutions are only specific solutions.
In accordance with another preferred embodiment of the invention, asymmetric inversion pulses are provided. Such pulses may be based on asymmetric solutions of the above hyper solutions. Asymmetric hyper-solutions result when parameter a is not zero. The magnetization profiles of asymmetric pulses are characterized as having a narrow transition (magnetization changes rapidly with frequency) and a broad transition (magnetization changes slowly with frequency). Two asymmetric solutions can be mirror images, with one having a narrow transition on the lower frequencies and one having a narrow transition on the higher frequencies. The inventors have determined that the narrow transition of a hyper pulse can be as narrow as ⅔ of the width of a sech/tanh pulse of a similar duration. In particular, over the range 1 less than a/b less than 500, a similar duration hyper-pulse has a narrow transition which is at least 20% narrower than a transition of a corresponding sech/tanh pulse. This is possible, because the width of one transition may be traded of with the width of the other transition, so it is possible to achieve narrow transition widths only where they are needed and not where they are not needed.
An FM pulse having a narrow transition is very useful. The following uses include a partial list of applications for such a pulse. Thus, an asymmetric pulse may be used for:
(a) fat suppression, as described above;
(b) population inversion, using a shorter duration pulse;
(c) population inversion, using a weaker Z gradient field;
(d) frequency selective inversion, for example, in NMR/MRI spectroscopy;
(e) inversion pulses of tip angles other than 180xc2x0, such as 90xc2x0;
(f) slice selection where a sharply defined border is required, such as in blood suppression in MRI angiography; and
(g) increased definition in MRI microscopy.
In accordance with another aspect of the present invention, the peak RF amplitude of the pulse is reduced from what would otherwise be necessary to yield the fastest transition. Moreover, the inventors have determined that, the peak amplitude requirement may be substantially reduced without overly increasing the width of the narrow transition.
There is therefore provided in accordance with a preferred embodiment of the invention a method of NMR (nuclear magnetic resonance) excitation of a sample having a magnetic moment, including:
applying a longitudinal magnetic field to the sample; and
changing the magnetic moment in a substantially continuous manner by moving an effective magnetic-field vector xcfx89e more than 90xc2x0, where for all portions of the sample in which the moment is changed, the angular velocity of the effective field vector at at least one angle, 90xc2x0+xcex1, is different from the angular velocity at 90xc2x0xe2x88x92xcex1. Preferably, changing the moment includes rotating the moment by approximately 180 degrees. Preferably, moving the magnetic-field vector includes applying an FM pulse and vector xcfx89e has components xcfx89x, xcfx89y and xcfx89z and changing includes changing according to the following formula:                               ω          x                =                              ω            1                    =                                    Ω              0                        ⁢                          xe2x80x83                        ⁢                                                            z                  ⁡                                      (                                          1                      -                      z                                        )                                                                              az                +                b                                                                                      ω          y                =        0                                          ω          z                =                              ω            -                          ω              0                                =                                                    cz                +                d                                            az                +                b                                      ⁢                          xe2x80x83                        -                          ω              0                                          
where, the frame of reference for the formula is a frame rotating at the instantaneous frequency of the FM pulse and where z is selected from the range 0 to 1 and where a time variable t is given by:   t  =      ln    ⁢          xe2x80x83        ⁢                  z        b                              (                      1            -            z                    )                          a          +          b                    
where a, b, c, d and xcexa90 are parameters having real values and where at least one of a, b, c, d, and xcexa90 are changed during the pulse. Preferably, cxe2x89xa00 or dxe2x89xa00.
In a preferred embodiment of the invention, vector xcfx89e has components xcfx89x, xcfx89y and xcfx89z and changing includes changing according to the following formula:                               ω          x                =                              ω            1                    =                                    Ω              0                        ⁢                          xe2x80x83                        ⁢                                                            z                  ⁡                                      (                                          1                      -                      z                                        )                                                                              az                +                b                                                                                      ω          y                =        0                                          ω          z                =                              ω            -                          ω              0                                =                                                    cz                +                d                                            az                +                b                                      ⁢                          xe2x80x83                        -                          ω              0                                          
where, the frame of reference for the formula is a frame rotating at the instantaneous frequency of the FM pulse and where z is selected from the range 0 to 1 and where a time variable t is given by:   t  =      ln    ⁢          xe2x80x83        ⁢                  z        b                              (                      1            -            z                    )                          a          +          b                    
where a, b, c, d and xcexa90 are parameters having real values and where axe2x89xa00, and (cxe2x89xa00 or dxe2x89xa00).
Preferably, 1xe2x89xa6a/bxe2x89xa61000. More preferably, 5xe2x89xa6a/bxe2x89xa6500. Further preferably, a/b is substantially equal to 11.09.
Preferably, changing the moment includes, moving the effective magnetic field vector both forwards and backwards.
There is also provided in accordance with a preferred embodiment of the invention a method of NMR (nuclear magnetic resonance) excitation of a sample having a magnetic moment, including:
applying a longitudinal magnetic field to the sample;
changing the magnetic moment in a continuous manner using an FM pulse; and
varying an effective magnetic-field vector xcfx89e having components xcfx89x, xcfx89y and xcfx89z and associated with the FM pulse, according to the following formula:                               ω          x                =                              ω            1                    =                                    Ω              0                        ⁢                          xe2x80x83                        ⁢                                                            z                  ⁡                                      (                                          1                      -                      z                                        )                                                                              az                +                b                                                                                      ω          y                =        0                                          ω          z                =                              ω            -                          ω              0                                =                                                    cz                +                d                                            az                +                b                                      ⁢                          xe2x80x83                        -                          ω              0                                          
where, the frame of reference for the formula is a frame rotating at the instantaneous frequency of the FM pulse and where z is selected from the range 0 to 1 and where a time variable t is given by:   t  =      ln    ⁢          xe2x80x83        ⁢                  z        b                              (                      1            -            z                    )                          a          +          b                    
where a, b, c, d and xcexa90 are parameters having real values and where axe2x89xa00, and (cxe2x89xa00 or dxe2x89xa00).
Preferably, 1xe2x89xa6a/bxe2x89xa61000. More preferably, 5xe2x89xa6a/bxe2x89xa6500. Further preferably, a/b is substantially equal to 11.09.
These is also provided in accordance with a preferred embodiment of the invention a method of NMR (nuclear magnetic resonance) excitation of a sample having a magnetic moment, including:
applying a longitudinal magnetic field to the sample; and
inverting the magnetization of at least a portion of the sample using an FM pulse having a duration, where a resulting magnetization profile Mz of the sample has at least a narrow transition and a broad transition.
Preferably, the magnetization profile has the formula                                           M            z                    =                                                                      sinh                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                  r                  ⁢                                      xe2x80x83                                    ⁢                  sinh                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                  v                                +                                  cos                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                  q                                                            cosh                ⁢                                  xe2x80x83                                ⁢                π                ⁢                                  xe2x80x83                                ⁢                r                ⁢                                  xe2x80x83                                ⁢                cosh                ⁢                                  xe2x80x83                                ⁢                π                ⁢                                  xe2x80x83                                ⁢                v                                      ⁢                          xe2x80x83                        ⁢            where                          ,                                                                    r              =                              d                -                                                      ω                    0                                    ⁢                  b                                                                                                        v              =                                                (                                      c                    +                    d                                    )                                -                                                      ω                    0                                    ⁡                                      (                                          a                      +                      b                                        )                                                                                                                          q              =                                                1                  2                                ⁢                                  xe2x80x83                                ⁢                                                                            Ω                      0                      2                                        -                                                                  (                                                  c                          -                                                                                    ω                              0                                                        ⁢                            a                                                                          )                                            2                                                                                                              
where a, b, c, d and xcexa90 are parameters having real values, xcfx890 is the Larmor frequency and where axe2x89xa00, and (cxe2x89xa00 or dxe2x89xa00), where if q is imaginary,       M    z    =                              sinh          ⁢                      xe2x80x83                    ⁢          π          ⁢                      xe2x80x83                    ⁢          r          ⁢                      xe2x80x83                    ⁢          sinh          ⁢                      xe2x80x83                    ⁢          π          ⁢                      xe2x80x83                    ⁢          v                +                  cosh          ⁢                      xe2x80x83                    ⁢          2          ⁢          π          ⁢                      "LeftBracketingBar"                          xe2x80x83                        ⁢            q            "RightBracketingBar"                                      cosh        ⁢                  xe2x80x83                ⁢        π        ⁢                  xe2x80x83                ⁢        r        ⁢                  xe2x80x83                ⁢        cosh        ⁢                  xe2x80x83                ⁢        π        ⁢                  xe2x80x83                ⁢        v              .  
Preferably, the width of the narrow transition is less than 0.9 of the width of a transition of a sech/tanh pulse having a similar duration and a narrowest possible transition. Further preferably, the width of the narrow transition is less than 0.75 of the width of a transition of a sech/tanh pulse having a similar duration and a narrowest possible transition. More preferably, the width of the narrow transition is less than 0.68 of the width of a transition of a sech/tanh pulse having a similar duration and a narrowest possible transition.
Preferably, the duration of the pulse is less than 0.9 of the duration of a sech/tanh pulse having a similar transition width thereto. More preferably, the duration of the pulse is less than 0.75 of the duration of a sech/tanh pulse having a similar transition width thereto. Further preferably, the duration of the pulse is less than 0.68 of the duration of a sech/tanh pulse having a similar transition width thereto.
Preferably, RF radiation emitted by the sample is detected after the moment is changed.
There is also provided in accordance with a preferred embodiment of the invention, a method of NMR (nuclear magnetic resonance) excitation of a sample having a magnetic moment and including a first material having nuclei associated thereto and at least a second material having nuclei associated thereto, including:
selectively changing the magnetic moment of only the nuclei associated with the first material using the methods described above. Preferably, an NMR/MRI sequence is applied to the sample after the magnetic moment of the nuclei associated with the first material is substantially zero. Preferably, the first material consists essentially of fat. Alternatively, the first material consists essentially of water. Further alternatively, the first material consists essentially of silicon.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an asymmetric pulse from an adiabatic FM pulse having modulation functions and an angular velocity profile, including, multiplying at least one modulation function by an asymmetric function.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an asymmetric pulse from an adiabatic FM pulse having modulation functions and an angular velocity profile, including, multiplying the angular velocity profile by an asymmetric function.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an asymmetric pulse from an adiabatic FM pulse having modulation functions and an angular velocity profile, including, optimizing at least one modulation function in an asymmetric manner.
There is also provided in accordance with a preferred embodiment of the invention, a method of creating an asymmetric pulse from an adiabatic FM pulse having modulation functions and an angular velocity profile, including, optimizing the angular velocity profile in an asymmetric manner.
Preferably, the asymmetric pulse has an effective magnetic field vector and the vector sweeps both forwards and backwards.